Boolean expression is an expression which involves Boolean operators and the final result of the expression is usually
represented by a Boolean value which is either a true statement (T) or a false statement (F). Boolean expressions have
their simplification rules and Boolean expression calculator helps us in getting an easy and quick final result.
Example 1: Prove that A + A B = A + B
So starting from the left side of the equation,A + A B
Now according to the Identity law, A T + A B
According to another Identity law A (T + B) + A B
According to Distributive law A T + A B + A B
According to Identity law A + B (A + A)
According to Complement law A + B T
According to Identity law A + B Hence proved!
Example 2: Simplify the given Boolean expression: B + (AB)
In order to simplify the above given Boolean expression, we have to use the Simplification laws of Boolean expressions.
According to DeMorgan’s Law, we have AB = A + B
So B + (A + B)
Now using the Commutative law we get B + (B + A),
Using the Associative law we get (B + B) + A
Using the Complement law we get, T + A
According to Identity law, T + A = T